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Title: | Existence of a nontrivial solution for the (p, q) Laplacian in RN without the Ambrosetti–Rabinowitz condition |
Keywords: | Equação de Laplace Ambrosetti-Rabinowitz condition Cerami condition Nontrivial weak solution (p, q)-Laplacian equations Condição de Ambrosetti-Rabinowitz Solução fraca não trivial |
Issue Date: | Feb-2015 |
Publisher: | Elsevier |
Citation: | CHAVES, M. F.; ERCOLE, G.; MIYAGAKI, O. H. Existence of a nontrivial solution for the (p, q) Laplacian in RN without the Ambrosetti–Rabinowitz condition. Nonlinear Analysis: Theory, Methods & Applications, [S.I.], v. 114, p. 133-141, Feb. 2015. DOI: https://doi.org/10.1016/j.na.2014.11.010. |
Abstract: | In this paper we prove the existence of at least one nonnegative nontrivial weak solution in D1,p (R N ) ∩ D1,q (R N ) for the equation −∆pu − ∆qu + a(x)|u| p−2 u + b(x)|u| q−2 u = f(x, u), x ∈ R N , where 1 < q < p < q ⋆ := Nq N−q , p < N, ∆mu := div(|∇u| m−2 ∇u) is the m-Laplacian operator, the coefficients a and b are continuous, coercive and positive functions, and the nonlinearity f is a Carathéodory function satisfying some hypotheses which do not include the Ambrosetti–Rabinowitz condition. |
URI: | https://doi.org/10.1016/j.na.2014.11.010 http://repositorio.ufla.br/jspui/handle/1/45525 |
Appears in Collections: | DEX - Artigos publicados em periódicos DMM - Artigos publicados em periódicos |
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